In this article, we investigate sufficient conditions of the existence of at least three positive solutions for a class of nonlinear fractional differential equations with three-point boundary value problems. Some new multiplicity and nonexistence results of positive solutions are established by using Leggett-Williams fixed point theorem on cones together with some comparison results. Finally, an example is presented to demonstrate the validity of the main results here.

existence, positive solution, boundary value problem, fractional differential equation.